Subgroups — #14518261

Order 1944.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11757860	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#4208	C₃	1	1	yes	maximal, characteristic
3	D₃×C₂²⋊C₂₇	—	3	4	no	maximal
4	#92319	—	4	1	no	maximal
5	C₂²×#737	C₂×C₃	1	1	yes	characteristic
6	C₂×#4208	—	3	1	no	—
7	C₂×#4208	—	3	1	no	—
8	#66353	—	2	4	no	—
9	C₃×C₂²⋊C₂₇	D₃	1	4	yes	complemented
10	#6903	—	4	1	no	Sylow
11	C₂²×#272	C₉	1	1	yes	characteristic
12	C₂²×D₃×C₉	—	3	4	no	—
13	C₂×C₂²⋊C₂₇	—	9	1	no	—
14	C₂×#737	—	3	1	no	—
15	#4208	—	3	1	no	—
16	#4208	A₄	1	1	yes	characteristic
17	D₃×C₂₇	—	12	4	no	—
18	C₂²×3₋¹⁺²	—	2	4	no	—
19	C₂²×H(3,𝔽₃)	C₂×C₉	1	1	yes	characteristic
20	C₂²×C₃×C₉	C₃×D₃	1	4	yes	—
21	C₂×#272	—	3	1	no	—
22	C₂×#272	—	3	1	no	—
23	C₂×D₃×C₉	—	9	4	no	—
24	C₂×D₃×C₉	—	9	4	no	—
25	C₂²⋊C₂₇	—	2	4	no	—
26	C₂²⋊C₂₇	C₃⋊D₃	1	1	yes	characteristic
27	#737	C₂×A₄	1	1	yes	characteristic
28	C₂₇⋊C₃	—	8	4	no	—
29	C₃×C₂₇	—	4	4	no	—
30	C₂²×C₃×D₃	—	3	4	no	—
31	C₂³×C₉	—	9	1	no	—
32	C₂×3₋¹⁺²	—	6	4	no	—
33	C₂×H(3,𝔽₃)	—	3	1	no	—
34	C₂×C₃×C₉	—	3	4	no	—
35	#272	—	3	1	no	—
36	#272	C₂²⋊C₉	1	1	yes	characteristic
37	D₃×C₉	—	3	4	no	—
38	D₃×C₉	—	9	4	no	—
39	C₂×C₂₇	—	36	1	no	—
40	C₂²×C₃²	D₃×C₉	1	4	yes	—
41	C₂×C₃×D₃	—	9	4	no	—
42	C₂×C₃×D₃	—	9	4	no	—
43	C₂²×C₉	—	2	4	no	—
44	C₂²×C₉	—	27	1	no	—
45	C₂²×C₉	—	27	1	no	—
46	C₂²×C₉	C₃×C₃⋊D₃	1	1	yes	characteristic
47	3₋¹⁺²	—	2	4	no	—
48	H(3,𝔽₃)	C₂×C₂²⋊C₉	1	1	yes	characteristic
49	C₃×C₉	D₃×A₄	1	4	yes	—
50	C₂₇	—	4	1	no	—
51	C₂₇	—	8	4	no	—
52	C₂³×C₃	—	9	1	no	—
53	C₂²×D₃	—	3	4	no	—
54	C₂×C₃²	—	3	4	no	—
55	C₃×D₃	—	3	4	no	—
56	C₃×D₃	—	9	4	no	—
57	C₂×C₉	—	3	1	no	—
58	C₂×C₉	—	6	4	no	—
59	C₂×C₉	—	9	1	no	—
60	C₂×C₉	—	27	1	no	—
61	C₂²×C₃	—	3	4	no	—
62	C₂²×C₃	—	27	1	no	—
63	C₂²×C₃	—	27	1	no	—
64	C₂²×C₃	C₉×C₃⋊D₃	1	1	yes	characteristic
65	C₂×D₃	—	9	4	no	—
66	C₂×D₃	—	9	4	no	—
67	C₃²	D₃×C₂²⋊C₉	1	4	yes	—
68	C₉	—	2	4	no	—
69	C₉	A₄×C₃⋊D₃	1	1	yes	characteristic
70	C₂³	—	9	1	no	Sylow
71	C₂×C₃	—	3	1	no	—
72	C₂×C₃	—	9	4	no	—
73	C₂×C₃	—	9	1	no	—
74	C₂×C₃	—	27	1	no	—
75	D₃	—	3	4	no	—
76	D₃	—	9	4	no	—
77	C₂²	—	27	1	no	—
78	C₂²	—	27	1	no	—
79	C₂²	#92319	1	1	yes	characteristic, complemented
80	C₃	—	3	4	no	—
81	C₃	C₃⋊D₃×C₂²⋊C₉	1	1	yes	characteristic
82	C₂	—	3	1	no	—
83	C₂	—	9	1	no	—
84	C₂	—	27	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₉	A₄×C₃⋊D₃
commutator, hypocenter	C₂²×H(3,𝔽₃)	C₂×C₉
Fitting, cosocle	C₂²×#737	C₂×C₃
socle	C₂²×C₃	C₉×C₃⋊D₃
prime radical	C₂²×#272	C₉
LCS	G ▷ C₂²×H(3,𝔽₃)
UCS	C₁ ◁ C₉

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. #11757860	C₂	semidirect
9. C₃×C₂²⋊C₂₇	D₃	semidirect
79. C₂²	#92319	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#11757860	2
C₂²×#4208	3
D₃×C₂²⋊C₂₇	3
#92319	4